Linear Models: A Mean Model Approach (Probability and Mathematical Statistics)

Linear models, normally presented in a highly theoretical and mathematical style, are brought down to earth in this comprehensive textbook. Linear Models examines the subject from a mean model perspective, defining simple and easy-to-learn rules for building mean models, regression models, mean vectors, covariance matrices and sums of squares matrices for balanced and unbalanced data sets. The author includes both applied and theoretical discussions of the multivariate normal distribution, quadratic forms, maximum likelihood estimation, less than full rank models, and general mixed models. The mean model is used to bring all of these topics together in a coherent presentation of linear model theory.

• Provides a versatile format for investigating linear model theory, using the mean model
• Uses examples that are familiar to the student:
• Design of experiments, analysis of variance, regression, and normal distribution theory
• Includes a review of relevant linear algebra concepts
• Contains fully worked examples which follow the theorem/proof presentation

Professor William Moser is a Professor of Chemical Engineering at the Worcester Polytechnic Institute. He is also a member of the Center for Inorganic Membrane Studies at WPI. Professor Moser invented both the Cylindrical Internal Reflectance Reactors (CIR-REACTORS) and Optical Fiber coupled CIR-Reactors (OFCIR-REACTORS), which are now commercial products used for reaction monitoring in homogeneous and heterogeneous catalysis. He was recently issued a patent on remote infrared sensing using optical fiber cables connected to high pressure reactors as well as normal laboratory glassware reactors. Dr. Moser is a Fellow of the New York Academy of Sciences, and is a co-founder of the Organic Reactions Catalysis Society. He is a past Chairman of the ACS Petroleum Division. He is the editor of several books on homogeneous and heterogeneous catalysis, and has a variety of publications and patents in the catalytic and materials science fields.

Zbynek Šidák was Chairman, Department of Probability and Statistics at the Mathematical Institute, Academy of Sciences, Czech Republic. He is now the principal research worker there. He has worked at various American universities as well. For 30 years, he was Editor of the journal Applications of Mathematics. His interests in statistics were rank tests, multivariate and cluster analysis, ranking and selection procedures, and Markov chains.

Pranab K. Sen is Cary C. Boshamer Professor of Biostatistics and Statistics at the University of North Carolina, and is a Fellow of the Institute of Mathematical Statistics and of the American Statistical Association. He is also an elected member of the International Statistical Institute.Prenab K. Sen is author or co-author of multiple volumes in Mathematical Statistics, Probability Theory and Biostatistics, and has published extensively in nonparametrics, multivariate and sequential analysis, and reliability and survival analysis.